<?xml version="1.0"?><?xml-stylesheet type="text/xsl" href="/Pages/Form4.xsl"?>
<ownershipDocument>

    <schemaVersion>X0304</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2011-08-19</periodOfReport>

    <issuer>
        <issuerCik>0000093751</issuerCik>
        <issuerName>STATE STREET Corp</issuerName>
        <issuerTradingSymbol>STT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001143422</rptOwnerCik>
            <rptOwnerName>SUMME GREGORY L</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O STATE STREET CORPORATION</rptOwnerStreet1>
            <rptOwnerStreet2>ONE LINCOLN STREET</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02111</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2011-08-19</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>31.99</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>49565</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares were purchased in multiple transactions at prices ranging from $31.98 to $32.00, inclusive. The reporting person undertakes to provide to State Street Corporation, any security holder of State Street Corporation, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the ranges set forth in this footnote 1.</footnote>
        <footnote id="F2">Includes Director's stock compensation dividend equivalents acquired through the date of this report.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jeremy Kream</signatureName>
        <signatureDate>2011-08-23</signatureDate>
    </ownerSignature>
</ownershipDocument>
